Aligned multiple flat mirror reflector array for concentrating sunlight onto a solar cell

ABSTRACT

An aligned multiple flat mirror reflector array for concentrating sunlight onto a solar cell is disclosed. The reflector array includes a concentrating dish and a plurality of flat mirrors disposed on an inside surface of the concentrating dish, the plurality of flat mirrors being disposed and aligned on the inside surface of the concentrating dish such that sunlight impinging upon each of the plurality of flat mirrors is reflected upon the solar cell.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application claims priority under 35 U.S.C. 119(e) from provisional patent application Ser. No. 60/997,253, entitled “Aligned Multiple Flat Mirror Reflectors Array To Concentrate Sunlight Onto Solar Cell”, filed on Oct. 1, 2007, the disclosure of which is herein incorporated by reference in its entirety.

BACKGROUND OF THE INVENTION

The present invention relates generally to solar reflector arrays and more particularly to an aligned multiple flat mirror reflector array for concentrating sunlight onto a solar cell.

The use of reflectors for focusing sunlight are well know. For example, U.S. Pat. No. 6,042,240 entitled “Adjustable Three Dimensional Focal Length Tracking Reflector Array” discloses a reflector positioned in orbit about a celestial body to focus sunlight on objects such as space debris to heat up and vaporize such debris. The reflector includes a plurality of units in an array, with each of the units including a plurality of subunits. Each of the units rotates about a first axis and each of the subunits is tiltable about a second axis which is perpendicular to the first axis. A reflecting surface is mounted on each of the subunits such that the reflecting surface rotates with its respective unit and tilts with its respective subunit. Each of the units and each of the subunits is independently controllable.

U.S. Patent Application Publication No. 2004/0074490 entitled “Solar Energy Reflector Array” discloses a heliostat comprising a reflector element and a carrier that is arranged to support the reflector element above a ground plane. A drive means is arranged to impart pivotal drive to the carrier about a fixed, first axis that is, in use of the heliostat, disposed substantially parallel to the ground plane. The heliostat further comprises a means mounting the reflector element to the carrier in a manner which permits pivotal movement of the reflector element with respect to the carrier and about a second axis that is not parallel to the first axis.

Known reflector arrays suffer the disadvantage that they are complex and thus expensive to manufacture and deploy. What is needed therefore is an aligned multiple flat mirror reflector array for concentrating sunlight onto a solar cell that is of relatively simple construction and inexpensive to manufacture and deploy.

SUMMARY OF THE INVENTION

In accordance with one aspect of the invention, an aligned multiple flat mirror reflector array for concentrating sunlight onto a solar cell includes a concentrating dish and a plurality of flat mirrors disposed on an inside surface of the concentrating dish, the plurality of flat mirrors being disposed and aligned on the inside surface of the concentrating dish such that sunlight impinging upon each of the plurality of flat mirrors is reflected upon the solar cell.

In accordance with another aspect of the invention, an aligned multiple flat mirror reflector array for concentrating sunlight onto a solar cell includes a concentrating dish and a plurality of panels disposed on an inside surface of the concentrating dish, the plurality of panels being disposed and aligned on the inside surface of the concentrating dish such that sunlight impinging upon each of the plurality of panels is reflected upon the solar cell, each of the plurality of panels comprises a plurality of flat mirrors.

In accordance with yet another aspect of the invention, an aligned multiple flat mirror reflector array for concentrating sunlight onto a solar cell includes a flat concentrating platform and a plurality of flat mirrors disposed on a surface of the flat concentrating platform, the plurality of flat mirrors being disposed and aligned on the flat surface of the concentrating platform such that sunlight impinging upon each of the plurality of flat mirrors is reflected upon the solar cell.

In accordance with another aspect of the invention, a method for concentrating sunlight onto a solar cell includes the steps of mounting a plurality of flat mirrors on a concentrating dish, and tilting and rotating the concentrating dish about first and second axes respectively such that each of the plurality of mirrors are aligned to reflect sunlight impinging thereon upon the solar cell.

There has been outlined, rather broadly, the more important features of the invention in order that the detailed description thereof that follows may be better understood, and in order that the present contribution to the art may be better appreciated. There are, of course, additional features of the invention that will be described below and which will form the subject matter of the claims appended herein.

In this respect, before explaining at least one embodiment of the invention in detail, it is to be understood that the invention is not limited in its application to the details of design and to the sequence of steps and processes set forth in the following description or illustrated in the drawings. The invention is capable of other embodiments and of being practiced and carried out in various ways. Also, it is to be understood that the phraseology and terminology employed herein, as well as the abstract, are for the purpose of description and should not be regarded as limiting.

As such, those skilled in the art will appreciate that the conception upon which this disclosure is based may readily be utilized as a basis for the designing of other structures and methods for carrying out the several purposes of the present invention. It is important, therefore, that the claims be regarded as including such equivalent structures and methods insofar as they do not depart from the spirit and scope of the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings:

FIG. 1 illustrates a perspective view of an aligned multiple flat mirror reflector array for concentrating sunlight onto a solar cell in accordance with the invention;

FIG. 2A illustrates a partial side elevation view of the reflector array of FIG. 1;

FIG. 2B illustrates a plan view of a concentrator dish in accordance with the invention;

FIG. 2C is a schematic representation of three flat mirrors of the concentrator dish of FIG. 2B;

FIG. 3 is a schematic representation of a plurality of flat mirrors of the concentrator dish of FIG. 2B;

FIG. 4A illustrates a plan view of a first alternative concentrator dish in accordance with the invention;

FIG. 4B illustrates a side elevation view of the concentrator dish of FIG. 4A;

FIG. 4C illustrates a panel of the concentrator dish of FIG. 4A;

FIG. 4D illustrates a side elevation view of the panel of FIG. 4C;

FIG. 5A illustrates a second alternative concentrator dish in accordance with the invention;

FIG. 5B illustrates a side elevation view of the concentrator dish of FIG. 5A;

FIG. 6A illustrates an expanded view of a corner panel of the concentrator dish of FIG. 5A;

FIG. 6B illustrates a side elevation view of the corner panel of FIG. 6A;

FIG. 7A illustrates a third alternative embodiment of the concentrator dish in accordance with the invention;

FIG. 7B illustrates a side elevation view of the concentrator dish of FIG. 7A;

FIG. 8 is a schematic representation of a plurality of flat mirrors of the concentrator dish of FIG. 7A;

FIG. 9 is a schematic representation of a flat mirror in relation to a solar cell in accordance with the invention;

FIG. 10A illustrates a reflected image on the solar cell in accordance with the invention;

FIG. 10B is a graph showing a light intensity distribution in accordance with the invention;

FIG. 11 is a table showing the relationship between mirror tilt angle and mirror width, reduced width, light projection, void space and cell width in accordance with the invention; and

FIG. 12 is a flow chart of a method for concentrating sunlight onto a solar cell in accordance with the invention.

DETAILED DESCRIPTION OF THE INVENTION

An aligned multiple flat mirror reflector array to concentrate sunlight onto a solar cell generally designated 100 is shown in FIG. 1 facing the sun. A concentrating dish 110 is fixedly attached to a support frame 120 that is in turn tiltably mounted to a rotatable post 130. Tilting of the concentrating dish 110 (indicated at arrow A) and rotation of the rotatable post 130 (indicated at arrow B) are programmably controlled by motors (not shown) to enable the concentrating dish 110 to follow the trajectory of the sun moving across the sky and maintain the concentrating dish 110 facing the sun. The concentrating dish 110 has a round, concave shape and preferably includes about 1000 flat mirrors that reflect parallel sunlight rays onto a solar cell 140 disposed above the center of the concentrating dish 110. The concentrating dish 110 effectively concentrates about 1000 times the intensity of the incident sunlight onto the solar cell 140.

With reference to FIG. 2A, the concentrating dish 110 is shown having a parabolic profile. The concentrating dish 110 is attached to the support frame 120 that is tiltable about an axis 210. Parallel sunlight rays are reflected onto the solar cell 140 by a plurality of mirrors 220 (FIG. 2B) arranged on the inside surface of the concentrating dish 110. The solar cell 140 is supported above the concentrating dish 110 by beams 230 attached to the support frame 120.

With reference to FIG. 2B, the concentrating dish 110 is shown having a round structure. 1064 square mirrors 220 are closely distributed on the inside surface of the concentrating dish 110 in covering relationship thereto and are arranged in vertical and horizontal lines. As illustrated in FIG. 2C, mirrors 220 a, 220 b and 220 c are aligned in three different directions. Each mirror 220 a, 220 b and 220 c reflects a square projection without focusing the light, however each mirror's direction is adjusted so that the light reflected thereby is concentrated at the solar cell 140.

FIG. 3 illustrates reflection onto the solar cell 140 by mirrors 300 a, 300 b, 300 c, and mirrors 220 a, 220 b and 220 c. Mirror 300 a is disposed perpendicular to the direction of the sun's rays and reflects the sun's rays perpendicularly to the solar cell 140. Mirror's 300 a, 300 c, 220 a, 220 b and 220 c are disposed at an angle to reflect the sun's rays onto the solar cell 140. To avoid blockage between mirrors, each mirror's position is raised in elevation along the extent of the inside surface of the concentrating dish 110 (represented in FIG. 3 by the curve 310) beginning with a lowest disposition of mirror 300 a and ending with a highest disposition of mirror 220 a. At the same time, the mirrors are tightly fitted against each other. The curve 310 is preferably parabolic or spherical in profile.

A first alternative embodiment of the invention is shown in FIGS. 4A-4D. A structured concentrating dish 400 includes a support network 410 for supporting multiple panels 420. The support network is supported within a tiltable mount structure 415. Each panel 420 includes a 4×4 array of flat mirrors 430 angled to face different directions. Mirrors 430 are mounted to a support 440. At the corner of each panel 420 is disposed a panel mount hole 450. Each panel 420 is screwed to elements of the support network 410 utilizing the mount holes 450.

A 7×7 array of panels 420 forms a square array 460 disposed in the middle of the support network 410. Disposed around the square array 460 are four panels 420 forming a roughly polygonal network 470 of panels 420. Following assembly of the structured concentrating dish 400, the 65 panels 420 provide 1040 mirrors 430 operable to reflect the sun's rays to a solar cell (not shown).

A second alternative embodiment of the invention is shown in FIGS. 5A and 5B. A concentrating dish 500 includes seven panels 505, 510, 515, 520, 525, 530 and 535. Panel 505 includes a 12×12 array of mirrors mounted to an inner ring 540 at contact points 540 a, 540 b and 540 c thereof. Panel 510 having 140 mirrors is mounted at contact points 550 a and 550 b of an outer ring 550 and at contact point 540 d of the inner ring 540. Panel 515 having 147 mirrors is mounted at contact points 550 c and 550 d of the outer ring 550 and at contact point 540 e of the inner ring 540. Panel 520 having 147 mirrors is mounted at contact points 550 e and 550 f of the out ring 550 and at contact point 540 f of the inner ring 540. Panel 525 having 140 mirrors is mounted at contact points 550 g and 550 h of an outer ring 550 and at contact point 540 g of the inner ring 540. Panel 530 having 147 mirrors is mounted at contact points 550 i and 550 j of the outer ring 550 and at contact point 540 h of the inner ring 540. Panel 535 having 147 mirrors is mounted at contact points 550 k and 550 m of the outer ring 550 and at contact point 540 i of the inner ring 540.

Panel 505 is mounted at three contact points of the inner ring 540 while each of panels 510, 515, 520, 525, 530 and 535 are mounted at two contact points of the outer ring 550 and one contact point of the inner ring 540. This triangular configuration provides support to the panels and a mechanism to finely align the panels by adjusting the spacing of the panels relative to the contact points.

With particular reference to FIG. 5B, inner and outer rings 540 and 550 are shown forming part of a support structure 560 for holding the panels 505, 510, 515, 520, 525, 530 and 535 in the proper orientation.

The triangular configuration of the second embodiment is further shown in FIG. 6A. Panel 515 is mounted to the outer ring 550 at contact points 550 c and 550 d, and to the inner ring 540 at contact point 540 e. Connection between the panel 515 and the contact point 540 e may include bolting the panel 515 to the contact point 540 e by means of bolt 600. Space between the contact point 540 e and the panel 515 provides adjustability to the orientation of the panel 515.

In accordance with the second embodiment of the invention, the inner and outer rings 540 and 550 are aligned concentrically and supported by a support frame 610. To achieve a concave structure, the outer ring 550 is disposed in a plane above the inner ring 540 relative to a tilt axis 620.

A third alternative embodiment of the invention is shown in FIGS. 7A and 7B. A square concentrating platform 700 includes a 32×32 array of mirrors 710 supported by a flat support structure 720. As shown in FIG. 8, mirrors 710 are disposed on the support structure 720 at different angles such that the sun's rays are reflected onto a solar cell 730 disposed a distance H from the support structure 720. The mirrors 710 are disposed a distance away from each other to avoid blocking the reflected light from adjacent mirrors 710 as illustrated by the positions of mirrors 710 a, 710 b and 710 c. Air conduits 740 may be provided between adjacent mirrors 710 to allow for air flow between adjacent mirrors 710 to thereby reduce wind drag and provide for a stable structure.

FIG. 9 illustrates reflection from a representative mirror 900 and projection onto a solar cell 910. To provide a square projection onto the solar cell 910 having a width d, a projected beam has a width d=d cos θ. The mirror 910 has an effective width d′=d cos θ/cos(θ/2).

With reference to FIG. 10A, a circular solar cell 1000 includes a square window 1010 coated with an anti-reflection material to allow transmission of light therethrough. Area 1030 is coated with a high reflection material to block transmission of light therethrough. Projections 1020 of light reflected from mirrors of the concentrating dishes of the invention are illustrated and the distribution of light intensity on the solar cell 1000 shown in FIG. 10B. Curve 1040 represents the total solar power distribution showing a high degree of uniformity across the solar cell 1000. Curve 1050 represents light intensity of a well aligned mirror while curve 1060 represents light intensity of a slightly misaligned mirror. Due to the fact that the reflected light is not focused by the mirrors, there are no hot spots on the solar cell 1000 and consequently no overheating or heat damage to the solar cell 1000.

In operation, the concentrating dish 110, 400, and 500 and concentrating platform 700 of the invention is tilted in a vertical direction and rotated horizontally to face the sun directly. Tilting of the concentrating dish 110, 400, and 500 and concentrating platform 700 is achieved by rotating the concentrating dish 110, 400, and 500 and concentrating platform 700 relative to an axis perpendicular to the rotatable post (rotatable post 130 in FIG. 1). Such tilting is achieved by means of a motor (not shown). In similar fashion, a motor (not shown) rotates the rotatable post. The two axes of rotation provide for tracking of the sun during each season.

Each of the concentrating dishes 110, 400, and 500 and concentrating platform 700 are comprised of a plurality of flat mirrors. Each mirror reflects an unfocused reflection of incident sun light onto a solar cell. The reflected light has a same shape as the mirror. The reflected light from the mirrors overlaps to enhance the illumination onto the solar cell by the number of mirrors used.

With reference to FIG. 3, for the mirror 300 c located at radius r and h from the solar cell 140, the mirror 300 c is tilted at an angle θ between the incident and reflected rays. The angle θ is also the projection angle for the reflected ray on the solar cell 140. The angle θ can be calculated from the dish structure and solar cell position H to be,

θ=tan⁻¹ [r/(H−h)].  (1)

The sunlight projection angle on the mirror is θ/2. With reference to FIG. 9, to keep the projected light on the solar cell 910 as a d by d square, the width of the mirror 900 having a tilted axis is reduced to,

d′=d cos θ/cos(θ/2).  (2)

The length remains unchanged. At the sunlight end,

d″=d cos θ  (3)

The ray of sunlight at mirror tilt axis is reduced too. Thus in the central locations of the concentrating dishes, little tilting is required and the mirrors have a generally square shape. For locations away from the central location, larger tilting is required and the effective areas of the mirrors have a rectangular or diamond shape.

As shown in FIG. 2A, the concentrating dish 110 includes the frame support 120 preferably formed of sheet metal or equivalent material. On the inside surface of the concentrating dish 110, 1000 mirror steps are made by plastic molding or sheet metal deforming. Each step is made with a specific tilting angle toward the central solar cell 140 in accordance with equation (1). Flat mirrors 220 are glued on the designed mirror steps. In principle, any flat mirror can be used. In practice, internal silver coated mirrors are most preferred. The soda lime glass is a preferred material for flat mirror glass because it has good solar transmission characteristics. Sunlight passes through the thin glass and is reflected by the silver coating in the glass to the solar cell 140. This provides a great advantage using the internal reflection in this particular application. The glass is the most durable protection layer for the mirror coating to last over all weather conditions outdoors. A dish is manufactured as a whole piece with support frame 120.

With reference to FIGS. 4A-4D, the concentrating dish 400 includes a framed network comprising 65 squares to support a plurality of panels 420. The framed network is joined onto the mount structure 415. Each mirror 430 of each panel 420 is oriented in a specific direction when manufactured. On the back side of each panel 420, there four panel mount holes 450 are disposed at the corners thereof. Each panel 420 has a rigid structure with sheet metal forming a back plate. Each panel 420 is made for its specific location on the concentrating dish 400 and can be installed in the field. This embodiment provides for simplified transportation and installation procedures.

The second embodiment of the invention shown in FIGS. 5A and 5B and in FIGS. 6A and 6B includes 1064 mirrors divided into 7 panels 505, 510, 515, 520, 525, 530 and 535, three panels 505, 510 and 525 having a near-square shape and disposed in a middle section of the concentrating dish 500, and four panels 515, 520, 530 and 535 having a near-triangle shape and disposed in top and bottom sections of the concentrating dish. Each panel 505, 510, 515, 520, 525, 530 and 535 is made on a rigid panel carrier with the mirrors attached thereto. The panels 505, 510, 515, 520, 525, 530 and 535 are manufactured in a process similar to the process described above with reference to panels 420. As previously described, each panel 505, 510, 515, 520, 525, 530 and 535 is mounted to the two ring mounting structure at 3 contact points. This three point mounting system advantageously provides for a stable structure and fine tuning of the alignment of the panel 505, 510, 515, 520, 525, 530 and 535. The two ring structure is simple and can be precisely made during the manufacture of the concentrating dish 500. The two rings 540 and 550 are connected to the support structure 560 to form a strong and rigid structure. In accordance with the second embodiment of the invention, a simple and durable structure is provided that reduces the work involved in transporting and installing the concentrating dish 500.

The third embodiment of the invention shown in FIGS. 7A and 7B and in FIG. 8 provides a 32×32 array of 1024 square mirrors d 710 distributed on the flat support structure 720. In this configuration there is provided a space between adjacent mirrors to avoid one mirror blocking the reflected light of the adjacent mirror. The minimum space between the edges of two adjacent mirrors is calculated as

v=d′ sin(θ/2)tan θ,  (4)

where d′ is the mirror width described in equation (2) and θ is the angle between incident light and reflected light. For the flat structure, θ is simply calculated as following.

θ=tan⁻¹(R/H).  (5)

In case of a tilt angle θ=45°, the mirror reduced width d′=0.765d, space v=0.383, d′=0.293d, sunlight projection d″=0.707d and cell width v+d″=d. The values for other tilt angles are listed in Table I shown in FIG. 11. As the mirror is tilted, the space between adjacent mirrors becomes larger and sunlight projection smaller. The cell width as the sum of the two is unchanged. The mirrors are distributed in even cells. The spaces between adjacent mirrors may advantageously be used as air conduits 740 to reduce wind drag. While the shape of the concentrating dish 700 has been described as square, those skilled in the art will recognize that other shapes are possible including hexagonal, octagonal or near-round shapes. In addition, mirrors can be grouped onto pre-mounted panels and the panels installed on the flat support structure 720 as described above.

In the above embodiments, on the order of 1000 flat mirrors are most preferred to achieve on the order of 1000 light concentration. Other numbers of flat mirrors, such as 100, 500, 1500, and 2000 can be employed to achieve different ratio concentrations. In one of preferred application, the mirror size is 100×100 mm² and 1000 mirrors form a concentrating dish covering a 10 m² area. In another preferred application, the concentrating dish can be made of roughly 1000 one square foot mirrors to cover an area of 1000 ft² or 100 m². In yet another preferred application, the concentrating dish can be made of roughly 1000 1″×1″ mirrors to cover an area of 2.5 m². For a given concentrating dish, the preferred solar cell height from the center of the concentrating dish is roughly half of the diameter of the concentrating dish.

A method for concentrating sunlight onto a solar cell generally designated 1200 is shown in FIG. 12. In a first step 1210 a plurality of flat mirrors are mounted on a concentrating dish. In a second step 1220 the concentrating dish is tilted and rotated about first and second axes respectively such that each of the plurality of mirrors are aligned to reflect sunlight impinging thereon upon the solar cell. The solar cell is preferably mounted a distance equal to half the diameter of the concentrating dish from a center of the concentrating dish. Mounting the plurality of flat mirrors on the concentrating dish comprises aligning each of the plurality of flat mirrors such that incident sunlight is reflected upon the solar cell.

It will be apparent to those skilled in the art that various modifications and variations can be made to the structure of the present invention without departing from the scope or spirit of the invention. In view of the foregoing, it is intended that the present invention cover modifications and variations of this invention provided they fall within the scope of the following claims and their equivalents. 

1. A solar reflector array for concentrating sunlight onto a solar cell comprising: a concentrating dish; and a plurality of flat mirrors disposed on an inside surface of the concentrating dish, the plurality of flat mirrors being disposed and aligned on the inside surface of the concentrating dish such that sunlight impinging upon each of the plurality of flat mirrors is reflected upon the solar cell.
 2. The solar reflector array of claim 1, wherein the solar cell is disposed a distance from a center of the concentrating dish.
 3. The solar reflector array of claim 1, wherein the concentrating dish is tiltable about a first axis and rotatable about a second axis perpendicular to the first axis.
 4. The solar reflector array of claim 3, wherein the concentrating dish is mounted to a support frame tiltable about the first axis.
 5. The solar reflector array of claim 1, wherein the concentrating dish has a parabolic profile.
 6. The solar reflector array of claim 1, wherein the concentrating dish has a spherical profile.
 7. A solar reflector array for concentrating sunlight onto a solar cell comprising: a concentrating dish; and a plurality of panels disposed on an inside surface of the concentrating dish, the plurality of panels being disposed and aligned on the inside surface of the concentrating dish such that sunlight impinging upon each of the plurality of panels is reflected upon the solar cell, each of the plurality of panels comprises a plurality of flat mirrors.
 8. The solar reflector array of claim 7, wherein the solar cell is disposed a distance from a center of the concentrating dish.
 9. The solar reflector array of claim 7, wherein the concentrating dish is tiltable about a first axis and rotatable about a second axis perpendicular to the first axis.
 10. The solar reflector array of claim 9, wherein the concentrating dish is mounted to a support frame tiltable about the first axis.
 11. The solar reflector array of claim 7, wherein each of the plurality of panels is adjustably mountable to a support structure comprising an inner ring and an outer ring, a first of the plurality of panels being mountable to three contact points of the inner ring, and each of the remaining plurality of panels being mountable to a contact point of the inner ring and two contact points of the outer ring.
 12. The solar reflector array of claim 11, wherein the inner ring has a smaller diameter than the outer ring and the outer ring is disposed in a plane above that of the inner ring relative to a tilt axis of the concentrator dish.
 13. A solar reflector array for concentrating sunlight onto a solar cell comprising: a flat concentrating platform; and a plurality of flat mirrors disposed on a surface of the flat concentrating platform, the plurality of flat mirrors being disposed and aligned on the flat surface of the concentrating platform such that sunlight impinging upon each of the plurality of flat mirrors is reflected upon the solar cell.
 14. The solar reflector array of claim 13, wherein the solar cell is disposed a distance from a center of the flat concentrating platform.
 15. The solar reflector array of claim 13, wherein the flat concentrating platform is tiltable about a first axis and rotatable about a second axis perpendicular to the first axis.
 16. The solar reflector array of claim 15, wherein the flat concentrating platform is mounted to a support frame tiltable about the first axis.
 17. A method for concentrating sunlight onto a solar cell comprising the steps of: mounting a plurality of flat mirrors on a concentrating dish; and tilting and rotating the concentrating dish about first and second axes respectively such that each of the plurality of mirrors are aligned to reflect sunlight impinging thereon upon the solar cell.
 18. The method of claim 17, further comprising mounting the solar cell a distance from a center of the concentrating dish.
 19. The method of claim 17, further comprising mounting the solar cell a distance roughly equal to half the diameter of the concentrating dish from a center of the concentrating dish.
 20. The method of claim 17, wherein mounting the plurality of flat mirrors on the concentrating dish comprises aligning each of the plurality of flat mirrors such that incident sunlight is reflected upon the solar cell. 